Meeta's Travel Path and Displacement

Let's track Meeta's movement step-by-step to find her final position relative to her starting point. We can imagine the starting point as the origin (0,0) on a coordinate system, where North is the positive y-axis, South is the negative y-axis, East is the positive x-axis, and West is the negative x-axis.

• Step 1: Meeta travels 4 km towards north.
• Starting at (0,0), moving 4 km North brings her to (0, 4).
• Step 2: She then travels 5 km eastward.
• From (0, 4), moving 5 km East brings her to (0 + 5, 4) = (5, 4).
• Step 3: She then travels 10 km rightwards. When facing East, rightwards is South.
• From (5, 4), moving 10 km South brings her to (5, 4 - 10) = (5, -6).
• Step 4: And then 3 km to the left. When facing South, left is East.
• From (5, -6), moving 3 km East brings her to (5 + 3, -6) = (8, -6).
• Step 5: And finally 5 km northwards.
• From (8, -6), moving 5 km North brings her to (8, -6 + 5) = (8, -1).

Her final position is at coordinates (8, -1). The starting point was (0,0).

Calculating Distance from the Original Destination

The displacement from the origin (0,0) to the final position (8, -1) can be found using the distance formula, which is based on the Pythagorean theorem. The horizontal displacement is 8 units (East) and the vertical displacement is -1 unit (South).

Distance = $\sqrt{(\text{Change in x})^2 + (\text{Change in y})^2}$

Distance = $\sqrt{(8 - 0)^2 + (-1 - 0)^2}$

Distance = $\sqrt{8^2 + (-1)^2}$

Distance = $\sqrt{64 + 1}$

Distance = $\sqrt{65}$ km

The value of $\sqrt{65}$ is approximately 8.06 km.

The question asks for the approximate distance.

Determining Direction from the Original Destination

The final position is at (8, -1). This means the final position is 8 units in the positive x-direction (East) and 1 unit in the negative y-direction (South) from the starting point (0,0).

A position that is East and South of the origin is in the South-East direction.

Final Displacement Summary

Meeta is approximately 8.06 km away from her original destination. The direction from the original destination to her final position is South-East.

Comparing this result with the given options:

• Option 1: 8 km towards east (Incorrect direction)
• Option 2: 15 km towards south (Incorrect distance and direction)
• Option 3: 8 km towards south-east (Approximately 8 km distance and South-East direction - Matches our calculation)
• Option 4: 18 km towards south (Incorrect distance and direction)

The approximate distance is 8 km and the direction is towards south-east.